There are given k stochastically ordered populations. A sequential sampling procedure (S) is proposed for selecting the population associated with the largest rank in the ordering. Observations are taken one at a time from each of the k populations. The procedure S allows for a specified maximum number (M) of observations to be taken from each population. The stage N at which the sampling is stopped depends on the choice of a parameter c. The choice of c is based on a trade-off between the expected number of observations and the probability of a correct selection (PCS). A table is given showing the values of c, the associated values of the PCS and the expected sample number, based on the asymptotic properties of S when M is large. Empirical results are given, based on a simulation study of the small sample properties of S.